As a conventional angular velocity sensor, well-known is the one disclosed in U.S. Pat. No. 5,438,231. The angular velocity sensor will be described with reference to FIG. 8.
FIG. 8 is a perspective view of a conventional angular velocity sensor. In FIG. 8, angular velocity sensor 101 comprises tuning-fork 102 made from non-piezoelectric material such as silicone, lower electrode 106 disposed on arm 103, arm 104, and substrate 105, lower electrode 107 disposed on arm 104, piezoelectric thin film 108 disposed on lower electrode 106, piezoelectric thin film 109 disposed on lower electrode 107, upper electrode 110 and upper electrode 111 disposed on piezoelectric thin film 108, upper electrode 112 and upper electrode 113 disposed on piezoelectric thin film 109. And, applying AC voltage the upper electrodes 110, 111, 112, and 113 causes the tuning-fork 102 to resonate.
The tuning-fork 102 of the above angular velocity sensor 101 has two perpendicular oscillation modes (an oscillation mode in the X direction and an oscillation mode in the Z direction). The tuning-fork 102 is driven in only one oscillation mode (for example, the oscillation mode in the X direction). In this condition, when rotational angular velocity is applied about the axis (Y axis) perpendicular to the axes (X axis, Z axis) of the two perpendicular oscillation modes, the tuning-fork 102 is excited in another (Z-direction) oscillation mode due to Corioli's force. The angular velocity sensor 101 utilizes this principle. In the configuration of such angular velocity sensor 101, in order to obtain a highly reliable detection signal with respect to the angular velocity applied, the resonance frequencies in the two perpendicular oscillation modes (the oscillation mode in the X direction and oscillation mode in the Z direction) of the tuning-fork 102 are required to be apart from each other. However, for improving the sensitivity of the detection signal with respect to the angular velocity applied, it is advantageous that the resonance frequencies in the two perpendicular oscillation modes (the oscillation mode in the X direction and the oscillation mode in the Z direction) of the tuning-fork 102 are close to each other. That is, from the viewpoint of reliability and sensitivity of the detection signal with respect to the angular velocity applied, it is desirable that the two resonance frequencies are close enough to each other so that they are free from coupling. However, regarding the sensitivity and reliability of the detection signal with respect to the angular velocity applied, there have been no documents that include considerations from the viewpoints of difference in elastic modulus depending upon the crystal orientation of the material for the tuning-fork and of resonance frequencies, including the above-mentioned U.S. Pat. No. 5,438,231.
The above-mentioned matter is described in detail in the following. Resonance frequency f is represented by (formula 1), where c is elastic modulus, ρ is density, d is arm width, and l is arm length.f∝√{square root over ((c/ρ))}*d/l2  (formula 1) 
In the above (formula 1), it is clear that the resonance frequency in the X-direction direction oscillation mode of the tuning-form 102 varies with elastic modulus c. In the case of the conventional angular sensor, there has been a problem that elastic modulus c in the X direction (driving direction) of the tuning-fork 102 varies depending upon the face selected as a crystal orientation at the side of arm 103, 104, resulting in variation of the sensitivity of detection signal with respect to the angular velocity applied and lowering the reliability.